Determining Order Lead Time for a Supply Chain Using a Probability Distribution of Order Lead Time

ABSTRACT

A system and method is disclosed for estimating demand of a supply chain including accessing a probability distribution of order lead time of the supply chain. The supply chain has nodes including a starting node and an ending node and a path from the starting node to the ending node. The probability distribution of order lead time describes ending node demand of the ending node versus order lead time. The path is divided into order lead time segments which are associated with the probability distribution of order lead time by associating each order lead time segment with an order lead time range of the probability distribution of order lead time. A demand percentage is estimated for each order lead time segment in accordance with the probability distribution of order lead time, such that each demand percentage describes a percentage of a total ending node demand of an order lead time segment.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part (CIP) of U.S. patentapplication Ser. No. 10/836,042, filed on Apr. 29, 2004 and entitled“Determining Order Lead Time for a Supply Chain Using a ProbabilityDistribution of Order Lead Time,” which claims the benefit of U.S.Provisional Patent Application Ser. No. 60/470,068, filed May 12, 2003,and entitled “Strategic inventory optimization.” U.S. patent applicationSer. No. 10/836,042 and U.S. Provisional Patent Application Ser. No.60/470,068 are commonly assigned to the assignee of the presentapplication. The disclosure of related U.S. patent application Ser. No.10/836,042 and U.S. Provisional Patent Application Ser. No. 60/470,068are hereby incorporated by reference into the present disclosure as iffully set forth herein.

BACKGROUND

1. Technical Field of the Invention

This invention relates generally to the field of supply chain analysisand more specifically to estimating demand for a supply chain accordingto order lead time.

2. Background of the Invention

A supply chain supplies a product to a customer, and may include nodesthat store inventory such as parts needed to produce the product. Aknown technique for maintaining a proper amount of inventory at eachnode may involve setting a reorder point at which inventory isreordered. For example, a node may reorder parts when its inventory isless than twenty units. Known techniques for maintaining a proper amountof inventory at each node, however, may require storage of excessinventory at the nodes and result in additional inventory carryingcosts. It is generally desirable to reduce excess inventory andassociated inventory carrying costs.

SUMMARY OF THE INVENTION

In accordance with the present invention, disadvantages and problemsassociated with previous supply chain analysis techniques may be reducedor eliminated.

According to one embodiment, estimating demand of a supply chainincludes accessing a probability distribution of order lead time of thesupply chain. The supply chain has nodes including a starting node andan ending node and a path from the starting node to the ending node. Theprobability distribution of order lead time describes ending node demandof the ending node versus order lead time. The path is divided intoorder lead time segments, and the order lead time segments areassociated with the probability distribution of order lead time byassociating each order lead time segment with a corresponding order leadtime range of the probability distribution of order lead time. A demandpercentage is estimated for each order lead time segment in accordancewith the probability distribution of order lead time in order toestimate demand for the supply chain. Each demand percentage describes apercentage of a total ending node demand associated with thecorresponding order lead time segment.

Certain embodiments of the invention may provide one or more technicaladvantages. For example, demand may be redistributed from an ending nodeto upstream nodes of a supply chain according to a probabilitydistribution of order lead time. Redistributing the demand to upstreamnodes may allow for optimizing inventory at individual nodes, which maysimplify the optimization. Inventory for the supply chain may beoptimized for the redistributed demand. Optimizing inventory forredistributed demand may decrease the need to stock inventory atdownstream nodes, which may minimize cost. Inventory may be optimizedwith respect to a probability distribution of order lead time for acustomer. Taking into account the order lead time may improve continuedperformance, which may lead to increased market share.

Certain embodiments of the invention may include none, some, or all ofthe above technical advantages. One or more other technical advantagesmay be readily apparent to one skilled in the art from the figures,descriptions, and claims included herein.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention and itsfeatures and advantages, reference is made to the following description,taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a block diagram illustrating an example system of optimizinginventory in a supply chain;

FIG. 2 is a flowchart illustrating an example method of optimizinginventory in a supply chain;

FIG. 3 illustrates an example matrix that may be used to generatecriticality groups;

FIG. 4 is a diagram illustrating an example supply chain that receivessupplies from one or more suppliers and provides products to one or morecustomers;

FIG. 5 is a flowchart illustrating an example method of inventoryoptimization;

FIGS. 6A through 6C illustrate example order lead time profiles;

FIG. 7 is a bar graph illustrating example cycle times for nodes of asupply chain;

FIG. 8 is a table with example demand percentages;

FIG. 9 is a diagram illustrating redistributed demand of an examplesupply chain;

FIG. 10 illustrates an example node for which an inventory may becalculated;

FIG. 11 illustrates an example supply chain that includes one nodesupplying another node;

FIG. 12 illustrates an example supply chain that includes one nodesupplying two nodes; and

FIG. 13 illustrates an example supply chain that includes two nodessupplying one node.

DESCRIPTION OF EXAMPLE EMBODIMENTS

FIG. 1 is a block diagram illustrating an example system 10 ofoptimizing inventory in a supply chain that supplies products tocustomers in response to customer demand. For example, system 10 mayoptimize target safety stocks or other inventory measures, within aminimum overall target customer service level (CSL), at each node in thesupply chain for each item flowing through the supply chain. Accordingto one embodiment, system 10 may use assumptions to formulate a supplychain model, and evaluate the assumptions with respect to historicalperformance. According to another embodiment, products may be segmentedinto policy groups, such as criticality groups, for example, in order todetermine customer service levels for the products. According to yetanother embodiment, order lead times may be used to redistributecustomer demand to upstream nodes of the supply chain.

According to the illustrated embodiment, system 10 includes a clientsystem 20, a server system 24, and a database 26 coupled as shown inFIG. 1. Client system 20 allows a user to communicate with server system24 to optimize inventory in a supply chain. Server system 24 managesapplications for optimizing inventory in a supply chain. Database 26stores data that may be used by server system 24.

According to the illustrated embodiment, server system 24 includes oneor more processors 30 and one or more engines 32 coupled as shown inFIG. 1. Processors 30 manage the operation of server system 24, and maycomprise any device operable to accept input, process the inputaccording to predefined rules, and produce an output. According to oneembodiment, processors 30 may comprise parallel processors in adistributed processing environment. Server system 24 may operate todecompose an optimization problem into a number of smaller problems tobe handled by a number of processors 30. As an example, server system 24may independently calculate the optimized inventory target for each of anumber of nodes using a different processor 30.

According to the illustrated embodiment, engines 32 include a demandmanager 33, a simulation engine 34, an analytics engine 36, anoptimization engine 38, and a supply chain planning engine 40. Engines32 may be configured in processors 30 in any suitable manner. As anexample, engines 32 may be located in different processors 30. Asanother example, a backup for an engine 32 and the engine 32 itself maybe located in different processors 30.

Demand manager 33 provides demand forecasting, demand planning, otherdemand management functionality, or any combination of the preceding.Simulation engine 34 simulates execution of a supply chain. Simulationengine 34 may be used to evaluate supply chain models. Analytics engine36 analyzes inventory, demand, and order lead time data. Analyticsengine 36 may be used to segment customers, items, locations, otherentities, or any combination of the preceding into policy groups fordifferent purposes. Optimization engine 38 optimizes the inventory atthe nodes of a supply chain. Demand may be distributed to upstream nodesaccording to a demand forecast, and optimization engine 38 may optimizeinventory for the distributed demand. Supply chain planning engine 40generates a plan for a supply chain.

Client system 20 and server system 24 may each operate on one or morecomputers and may include appropriate input devices, output devices,mass storage media, processors, memory, or other components forreceiving, processing, storing, and communicating information accordingto the operation of system 10. For example, the present inventioncontemplates the functions of both client system 20 and server system 24being provided using a single computer system, such as a single personalcomputer. As used in this document, the term “computer” refers to anysuitable device operable to accept input, process the input according topredefined rules, and produce output, for example, a personal computer,work station, network computer, wireless telephone, personal digitalassistant, one or more microprocessors within these or other devices, orany other suitable processing device.

Client system 20, server system 24, and database 26 may be integrated orseparated according to particular needs. If any combination of clientsystem 20, server system 24, or database 26 are separated, they may becoupled to each other using a local area network (LAN), a metropolitanarea network (MAN), a wide area network (WAN), a global computer networksuch as the Internet, or any other appropriate wire line, optical,wireless, or other link.

Modifications, additions, or omissions may be made to system 10 withoutdeparting from the scope of the invention. For example, system 10 mayhave more, fewer, or other modules. Moreover, the operations of system10 may be performed by more, fewer, or other modules. For example, theoperations of simulation engine 34 and optimization engine 38 may beperformed by one module, or the operations of optimization engine 38 maybe performed by more than one module. Additionally, functions may beperformed using any suitable logic comprising software, hardware, otherlogic, or any suitable combination of the preceding. As used in thisdocument, “each” refers to each member of a set or each member of asubset of a set.

FIG. 2 is a flowchart illustrating an example method of optimizinginventory in a supply chain. The method may be used to separate thedemand analysis from the supply analysis by redistributing the demand toupstream nodes and then calculating the inventory required to satisfythe redistributed demand. Separating the demand may provide for moreefficient inventory analysis. The method begins at step 48, where asupply chain model is formulated for a supply chain. A supply chainmodel may be used to simulate the flow of items through the supplychain, and may represent one or more constraints of a supply chain. Aconstraint comprises a restriction of the supply chain. The supply chainmodel may have one or more assumptions. An assumption comprises anestimate of one or more parameters of a supply chain model.

The assumptions are evaluated at step 50. The assumptions may beevaluated by simulating the supply chain using the supply chain modeland validating the simulation against historical data describing actualperformance of the supply chain. Historical data describing a first timeperiod may be applied to the supply chain model to generate a predictiondescribing a second time period. For example, given one year of data,the first ten months of data may be used with the supply chain model topredict the last two months of data. The prediction for the second timeperiod may be compared to the historical data describing the second timeperiod in order to evaluate the assumptions of the supply chain model.The assumptions may be adjusted in response to the evaluation.

The inventory is analyzed at step 52. The inventory may be analyzed bysegmenting products into policy groups such as criticality groups. Eachcriticality group may correspond to a particular inventory policy suchas a customer service level. Customer demand and order lead time mayalso be analyzed to determine demand and order lead time means andvariability. The inventory is optimized at step 54 to determine anoptimized inventory for each node of the supply chain. The sensitivityof the optimized inventory may be analyzed by adjusting the assumptionsand checking the sensitivity of the inventory to the adjustment.According to one embodiment, the assumptions may be relaxed in order toreduce the complexity of the optimization.

The optimization may be validated at step 56. During validation, anyassumptions that were relaxed during optimization may be tightened. Aninventory policy may be determined at step 58. According to oneembodiment, a user may decide upon an inventory policy in response tothe validation results. The inventory policy is implemented in thephysical supply chain at step 60.

The inventory performance may be evaluated at step 62 by determiningwhether the inventory performance satisfies inventory performancemeasures. In response to evaluating the inventory performance, themethod may return to step 48 to formulate another supply chain model, tostep 50 to re-evaluate the assumptions, to step 52 to re-analyze theinventory, or to step 58 to determine another inventory policy, or themethod may terminate. According to one embodiment, an actual customerservice level may be measured at a first time period. If the actualcustomer service level fails to satisfy the target customer servicelevel, deviations between actual and assumed input values may bedetermined. The deviations may be determined according to definedworkflows that are consistent and repeatable over successive timeperiods. An input value with a deviation may be identified to be a rootcause of the failure and this information used as feedback for asubsequent time period. During the subsequent time period, the assumedvalue for the identified input may be adjusted and used to calculate areoptimized inventory target. According to the embodiment, the steps ofthe method may be repeated in an iterative closed-loop process that isconsistent and repeatable over successive time periods. The iterativeclosed-loop process may use the assumed values of the inputs as itsinputs and the actual customer service level as its output.

Modifications, additions, or omissions may be made to the method withoutdeparting from the scope of the invention. For example, the step ofevaluating the assumptions may be omitted. Additionally, steps may beperformed in any suitable order without departing from the scope of theinvention. For example, the step of evaluating the assumptions may beperformed after the step of analyzing inventory. Furthermore, althoughthe method is described as optimizing inventory for each node of thesupply chain, the method may be used to optimize inventory for a subsetof one or more nodes of the supply chain.

FIG. 3 illustrates an example matrix Mi . . . j 66 that may be used togenerate policy groups such as criticality groups. A policy groupcomprises a set of entities strategically segmented for a particularpurpose. An entity may comprise, for example, a product, a location, ora customer of a supply chain. According to one embodiment, a policygroup may refer to a criticality group for which a service level policyis defined. A service level policy describes the level of service for anentity, and may include a customer service level, a lead time, or otherparameter. As an example, segmentation may classify customers intocriticality groups, where each criticality group has a specifiedcustomer service level. Criticality groups may be used to definedifferent service levels for different customers. According to anotherembodiment, another policy group may refer to a set of entities thatexhibit common buying behaviors, for example, common order lead timeprofiles.

According to the illustrated example, matrix M_(i . . . j) 66 is used tosegment products into criticality groups, where each entry, or cell,m_(i . . . j) represents a criticality group with a specific servicelevel policy. Matrix M_(i . . . j) 66 may have any suitable number ofindices i . . . j, where each index represents an attribute of theentities. An attribute comprises a feature of an entity that is relevantto the service level associated with the entity, and may be quantitativeor non-quantitative. Examples of quantitative attributes includeinventory volume, revenue calculated as volume times price, marginvolume calculated as price minus cost, or other attributes. Examples ofnon-quantitative attributes may include product tier or life cycle,number of customers served, or other attributes. According to theillustrated example, index i represents the relative speed with whichitems for the product move through the supply chain, and j representswhether there is a hub agreement with the nodes through which the itemsflow. An index may, however, represent any suitable attribute. As anexample, an index may be used to define target customer service levels,minimum offered lead times, maximum offered lead times, or anycombination of the preceding for each criticality group. Eachcriticality group may represent a unique combination of item, location,and channel.

As used herein, the term “matrix” is meant to encompass any suitablearrangement of attributes in which each attribute associated with thematrix corresponds to at least one index of the matrix and maycorrespond to any number of indexes of the matrix. Such a matrix mayhave any suitable format. As an example, different cells may havedifferent indices. As another example, policy groups corresponding todifferent cells may overlap. Membership to overlapping policy groups maybe resolved by, for example, assigning priorities to the policy groups.An attribute not corresponding to any index of the matrix may beassigned to a default policy group.

FIG. 4 is a diagram illustrating an example supply chain 70 thatreceives supplies from one or more suppliers 80 and provides products toone or more customers 84. Items flow through supply chain 70, and may betransformed or remain the same as they flow through supply chain 70.Items may comprise, for example, parts, supplies, or services that maybe used to generate the products. The products may include none, some,or all of some or all of the items. For example, an item may comprise apart of the product, or an item may comprise a supply that is used tomanufacture the product, but does not become a part of the product.Downstream refers to the direction from suppliers 80 to customers 84,and upstream refers to the direction from customers 84 to suppliers 80.

Supply chain 70 may include any suitable number of nodes 76 and anysuitable number of arcs 78 configured in any suitable manner. Accordingto the illustrated embodiment, supply chain 70 includes nodes 76 andarcs 78. Items from supplier 80 flow to node 76 a, which sends items tonode 76 b. Node 76 b sends items to node 76 c, which sends items tocustomer 84 a and nodes 76 d and 76 e. Nodes 76 d and 76 e provideproducts to customers 84 b and 84 c, respectively.

Node 76 a may comprise one of one or more starting nodes 76 a upstreamfrom one or more ending nodes 76 d-e. Starting nodes 76 a may receiveitems directly from supplier 80 or from an upstream node 76, and endingnodes 76 c-e may send items directly to a customer 84 a-c or to adownstream node 76. A starting node 76 a and an ending node 76 c-e maydefine a path that includes starting node 76 a, ending node 76 c-e, andany intermediate nodes 76 b-c between starting node 76 a and an endingnode 76 c-e.

Although supply chain 70 is illustrated as having five nodes 76 a-e andfour arcs 78 a-d, modifications, additions, or omissions may be made tosupply chain 70 without departing from the scope of the invention. Forexample, supply chain 70 may have more or fewer nodes 76 or arcs 78.Moreover, nodes 76 or arcs 78 may have any suitable configuration. Forexample, node 76 a may supply items to node 76 c, but not to node 76 b.As another example, any node 76 may supply items directly to a customer84.

The products may be delivered to a customer 84 according to an orderlead time or a demand lead time for customer 84. An order or demand leadtime represents the time period during which supply chain 70 may satisfyan order. That is, an order or demand lead time is the time between whenan order or demand is placed and when it needs to be served or when thedemand is fulfilled. For example, if an airline ticket is purchased fora trip that will take place in 4 days, then the order lead time is 4days. The airline knows the demand 4 days ahead of time. It is notedthat the order or demand lead time is different from the typical supplylead time, which is the time it takes for a supplier to replenish aproduct.

The order or demand lead time for customer 84 may be calculated as thetime between the time when the order or demand is finalized and the timewhen the order is to be provided to customer 84. The time when an orderis finalized may be different from the time when the order was placed,since the order may be modified before the order is finalized. Afinalized order may refer to an order at any suitable stage of thesupply chain process. For example, finalized orders may refer to lastchanged orders, orders that have been shipped, orders that are inbacklog, other suitable orders, or any combination of the preceding.

The order lead time for customer 84 may be described using a probabilitydistribution of order lead time. A probability distribution of orderlead time describes the probability distribution of demand relative toorder lead time. That is, a cumulative probability distribution of orderlead times is estimated by computing the cumulative percentage of orderor demand volume against order or demand lead times. A probabilitydistribution of order lead time may be calculated from an order leadtime profile. An order lead time profile describes demand with respectto order lead time, and may be generated from a demand profile thatdescribes demand with respect to time. The demand may be expressed asunit demand, as a proportion of the demand, or in any other suitablemanner. As an example, an order lead time profile may describe acumulative percentage of the demand with respect to order lead time. Forexample, an order lead time profile may have a y axis representing thecumulative percentage of demand and an x axis representing order leadtime expressed as number of days. An example order lead time profiles(i.e., a cumulative probably function of order lead time) is describedin more detail with reference to FIG. 6.

Although the probability distribution of order lead time may becalculated from an order lead time profile, the probability distributionmay be determined from other suitable types of information using anysuitable number of parameters. For example, the probability distributionmay be determined from the absolute demand volume with respect to time.As another example, the probability distribution may be determined usinga fuzzy logic approach. A fuzzy logic approach may, for example,designate that a certain amount or portion of the demand has a specificorder lead time.

All of the demand typically does not have the same order lead time. Thatis, the order lead time may vary for each order, such that, some ordersmay be placed well in advance, while other orders may be placed at thelast minute. For example, 70% of the demand may have an order lead timeof less than 20 days, and 30% of the demand may have an order lead timeof 20 days or greater. If a node 76 can replenish its inventory in timeto satisfy a portion of the demand, node 76 does not need to stock theinventory for that portion of the demand. For example, if node 76 canreplenish its inventory in less than 20 days to satisfy 30% of thedemand, node 76 does not need to stock inventory for 30% of the demand.

According to one embodiment, the demand initiated by a customer 84 maybe redistributed from a downstream node 76 to one or more upstream nodes76. For example, the demand initiated by customer 84 a, 84 b, or 84 cmay be redistributed from downstream node 76 c, 76 d, or 76 e,respectively, to one or more upstream nodes 76 a-c. Optimization of theredistributed demand may be postponed to upstream nodes 76 a-c.Redistributing demand upstream may serve to optimize supply chain 70.Typically, maintaining items at upstream nodes 76 is less expensive thanmaintaining items at downstream nodes 76. Additionally, more developeditems at downstream nodes 76 are typically more susceptible to marketchanges. A method of optimizing inventory by redistributing demand toupstream nodes 76 is described in more detail with reference to FIG. 5.

According to one embodiment, redistributing the demand upstream involvestaking into account the time it takes for supplies needed at nodes 76 tobe replenished and the reliability of the supply nodes 76. Thereplenishment time may be determined from supply lead times (SLTs).According to the illustrated example, the mean supply lead time(μ_(SLT)) for node 76 a is 20.0 days with a variability (s_(SLT)) of 6.0days, the mean supply lead time for arc 78 a is 1.5 days with avariability of 0.5 days, the mean supply lead time for node 76 b is 6.0days with a variability of 2.67 days, the mean supply lead time for node76 c is 0.0 days with a variability of 0.00 days, the mean supply leadtime for arc 78 b is 1.0 day with a variability of 0.33 days, and themean supply lead time for arc 78 c is 1.5 days with a variability of 0.5days. Node 76 c may be considered a global distribution node. Thereliability of the supply nodes 76 may be determined from the customerservice levels of nodes 76. According to the illustrated example, thecustomer service level for node 76 a is 80%, and the customer servicelevels for nodes 76 b and 76 c are 96%.

FIG. 5 is a flowchart illustrating an example method of inventoryoptimization using order lead time distributions. In one embodiment,order lead time or demand lead time is the time between when an order ordemand is placed and when it needs to be served. As a non-limitingexample and as discussed above, if an airline ticket is purchased for atrip that will take place in 4 days, then the order lead time is 4 days.The airline knows the demand 4 days ahead of time. As used herein, orderor demand lead time is different from supply lead time, which is thetime it takes for a supplier to replenish a product. Order lead time mayvary for each order, such that, some orders may be placed well inadvance, while other orders may be placed at the last minute. An orderlead time distribution is a probability distribution across the range ofall possible order lead times. Note that order lead time distribution isa distinct notion from the notion of probability distribution of demandwhich represents the magnitude of the demand during a particular timeand not how far in advance that demand was known.

The method begins at step 102, with a portfolio of ending node demandstreams. Ending nodes 76 (for example, nodes 76 d and 76 e) are definedas nodes in the supply chain that service independent demands (i.e.directly serving customers 84). An ending node demand stream is a timeseries of demands at an ending node forecasted over one or more timeperiods. The time periods may not need to be equal in length. In oneembodiment an ending node demand stream is identified by a uniquecombination product being sold, location from where the product is beingshipped from and customer or customer location to whom the product isbeing sold to.

Continuing with step 102, customers, products, locations, other entity,or any combination of the preceding may be organized into groups forcharacterizing order lead time. For example, customers 84 may becategorized according to features that affect the order lead times ofcustomers 84, such as demand requirements that customers 84 are requiredto satisfy, order lead times for the customer's industry, or otherfeatures. These features may be identified using a lead time history. Asanother example, product shipment size may be used to categorizeproducts, or channel efficiency may be used to categorize channels.

At step 104, discrete probability distributions are computed torepresent the distribution of order lead times within each order leadtime group. An example order lead time distribution is described in moredetail with reference to FIG. 6A. As described below, FIG. 6A is thecumulative probability density function of order lead time, alsoreferred to as the order lead time profile. For example, as shown inFIG. 6A a point Q indicates that 90% of the demand volume comes within30 days or less of order lead time. Another way to read the same point Qis that 10% of the demand volume will come with at least 30 days ofadvance notice.

An order lead time profile may be determined by identifying the categoryto which a specific customer 84 belongs, and selecting the order leadtime profile that corresponds to the identified category from the orderlead time profile options. According to one embodiment, the lead timeprofile for a specific order lead time group may be modified tocustomize the order lead time profile. As an example, the order leadtime profile may be modified by a user using a user interface to accountfor a predicted change in customer demand. The predicted change mayresult from, for example, item shortages, profit increase, economicdownturn, or other economic factor. As another example, the order leadtime profile may be modified to account for a maximum offered lead timeor a minimum offered lead time.

As discussed below, steps 108, 110, and 118 are performed for each endnode demand stream. At step 108, each distinct supply path is looked upfor the end node. For each path the cumulative supply lead time islisted out, with a specified confidence level from each upstreaminventory carrying node to the end node. As an example only and not byway of limitation and with reference to FIG. 4, nodes 76 a, 76 c, 76 dand 76 e are inventory carrying nodes and node 76 b is designated as anon-inventory carrying or “flow-through” node.

In this example, the supply lead time (SLT) for each order lead timesegment is calculated at step 108. According to one embodiment, thesupply lead time SLT for an order lead time segment may be calculatedaccording to SLT=μ+xσ for y % certainty. Values x and y may bedetermined according to standard confidence levels when SLT isrepresented as a normal distribution with a mean of μ and standarddeviation of σ. For example, x=3 for y=99. According to the examplesupply chain 70 of FIG. 4, for 99% certainty, the supply lead time forarc 78 c is 1.5+3(0.5)=3.0 days. Similarly, for 99% certainty, thesupply lead time for arc 78 b is 2.0 days, and the supply lead time forarc 78 a is 3.0 days. The supply lead time, however, may be calculatedaccording to any suitable formula having any suitable parameters. Forexample, the supply lead time SLT may be calculated according toSLT=p₁+p₂, where p₁ represents a minimum delay, and p₂ represents anadditional delay. Both p₁ and p₂ may be represented with their ownprobability distributions. Moreover, the supply lead times may have anysuitable relationship with each other. For example, at least two of thesupply lead times may overlap. Furthermore, the supply lead times may beadjusted in any suitable manner. For example, a one day padding may beadded to one or more supply lead times.

In this example, and assuming supply lead times of 99% confidence isdesired, supply chain 70 computes the supply lead time as μ+3σ for eachstep of the supply path. The cumulative supply lead times are shown inTABLE 1:

TABLE 1 List of Arches and nodes with Supply Lead Time Inventory SLTspecified with 99.9% confidence carrying making up supply from inventorycarrying node path to end node 76d node to end node 76d 76d none 0 76c78c 1.5 + 3 × 0.5 = 3 76a 78c, 78b, 76b, 78a [1.5 + 3 × 0.5] + [1 + 3 ×0.33] + [6 + 3 × 2.67] + [1.5 + 3 × 0.5] = 22

Supply chain 70 divides the order lead time distribution for the endnode into order lead time segments (OLTSs) corresponding to each supplylead time, at step 110. An order lead time segment represents a portionof the path of supply chain 70 that may be used to distribute order leadtimes and demand upstream. Cycle times may be used to establish theorder lead time segments. A cycle time for a node 76 or arc 78represents the difference between the time when an item arrives at thenode 76 or arc 78 and the time when the item leaves the node 76 or arc78. For example, the cycle time for a node 76 may include amanufacturing, production, processing, or other cycle time. The cycletime for an arc 78 may include a distribution, transportation, or othercycle time. A cumulative cycle time for a node 76 represents thedifference between the time when an item arrives at the node 76 and thetime when the end product is delivered to customer 84. A cumulativecycle time may include the sum of one or more individual cycle timesinvolved, for example, the cycle times for one or more nodes 76 and oneor more arcs 78 involved. As an example, an order lead time segment mayrepresent the difference between the cumulative cycle times for a firstnode 76 and an adjacent second node 76. Examples of order lead timesegments are described with reference to FIG. 7.

Assuming that the order lead time distribution for the order lead timegroup to which end node 76 d belongs is characterized by FIG. 6A, supplychain 70 computes order lead time segments in the following example. Inthis example, the supply lead time from node 76 c to node 76 d is 3days. Order Lead Time distribution at a point P indicates that there isa 33% probability that orders will come with order lead time of 3 daysor less. This is same as saying that 33% demand volume comes with 3 daysor less of order lead time. Continuing with this example, the supplylead time from node 76 a to node 76 d is 22 days. Order Lead Timedistribution at a point S indicates that there is a 81% probability thatorders will come with lead time of 22 days or less. Combining this withthe information for node 76 c there is a 48% probability that orderswill come in with lead times greater than 3 days but less than 22 days,as shown in TABLE 2:

TABLE 2 Inventory Order carrying Supply path to Lead Time Order LeadTime node end node 76d Segment Range Difference Demand % 76d none OLT 1=3 days 33-0  33% 76c 78c OLT 2 >3 days but = 22 days 81-33 48% 76a 78c,78b, 76b, OLT 3 >22 days 100-81  19% 78a

Once demand percentage splits along order lead time segments have beenobtained as shown in TABLE 2, supply chain 70 redistributes demand forthe purpose of inventory targets calculation. That is, if only 33% ofthe total demand at end node 76 d comes with an order lead time of 3days or less the safety stock needed at 76 d needs to guard against onlydemand variability for 33% of the total demand. The remaining 67% ofdemand will arrive with sufficient lead time that it can be sourced fromupstream inventory carrying nodes. This results in the ability topostpone safety stocks to upstream nodes.

Demand is redistributed to upstream order lead time segments at step 118in order to postpone safety stock inventory to upstream nodes 76. Demandmay be redistributed by estimating demand percentages for the order leadtime segments. A demand percentage for an order lead time segmentrepresents the percentage of the demand that needs to be satisfiedduring the order lead time segment in order to satisfy the customerdemand within the constraints of the order lead time profile. An exampleof calculating demand percentages is described with reference to FIGS. 8and 9.

Inventory that satisfies the demand percentages is established at nodes76 at step 120. By calculating a demand percentage for each order leadtime segment, the inventory for the redistributed demand may bedetermined by postponing safety stock inventory at each node 76. Theinventory may be determined by calculating the inventory required atending nodes 76 (for example, nodes 76 d and 76 e) to satisfy the demandpercentage of ending nodes 76. The calculated inventory generates ademand for a first upstream node 76 (for example, node 76 c). Theinventory at the first upstream node 76 is determined to generate ademand for a second upstream node 76 (for example, node 76 c), and soon. Inventory needed to satisfy the redistributed demand may be combinedwith inventory needed without regard to the redistributed demand inorder to determine the total demand needed at a node 76. A method forestablishing the inventory is described in more detail with reference toFIGS. 10 through 13.

Modifications, additions, or omissions may be made to the method withoutdeparting from the scope of the invention. For example, order lead timeprofiles need not be created for different categories at step 102.Instead, an order lead time profile for the specific customer 84 maysimply be retrieved. Additionally, steps may be performed in anysuitable order without departing from the scope of the invention.

FIGS. 6A through 6C illustrate example order lead time profiles. Anorder lead time profile describes a demand corresponding to a node 76such as an ending node 76 (for example, node 76 d or 76 e). For example,an order lead time profile may describe demand associated with customer84 a of FIG. 4. The customer demand is placed on ending node 76 d tofulfill. In the illustrated embodiment, the order lead time profile isunconstrained (that is, assumes unlimited supply). Although the exampleorder lead time profiles are illustrated as graphs, the information ofthe order lead time profiles may be presented in any suitable manner,for example, in a table.

FIG. 6A illustrates an example order lead time profile. According to theillustrated embodiment, a y axis 152 represents the cumulativepercentage of demand volume, and an x axis 154 represents the order leadtime expressed in days. According to one embodiment, a curve 160represents an example of an order lead time profile that describes thecumulative percentage of demand volume having a certain order lead time.Accordingly, a point (x, y) of curve 160 represents that cumulativepercentage y of the demand volume has an order lead time of x days. Forexample, a point P indicates that 33% of the demand volume has an orderlead demand time of less than 3 days, a point S indicates that 81% ofthe demand volume has an order lead demand time of less than 22 days, apoint Q indicates that 90% of the demand volume has an order lead timeof 30 days, and a point R indicates that 100% of the demand volume hasan order lead time of less than 60 days.

In one embodiment, order lead time profiles may be generated fordifferent group levels, for example, for all orders, all items, alllocations, or other group level. Generating order lead time profiles atthe group level may result in generating fewer profiles, which may beeasier to manage. Moreover, a user may be able to select a profile basedupon the group level of interest. In another embodiment, multiple orderlead time profiles may be generated for a group level. For example, anorder lead time profile may be generated for each item. Generatingmultiple order lead time profiles may allow for fine-tuned demandmonitoring. For example, where an order lead time profile is generatedfor each item, the order lead time profile for each item may beautomatically monitored for changes that may impact optimal inventorytarget levels.

FIGS. 6B and 6C illustrate example order lead time profiles customizedto account for maximum and minimum offered lead times, respectively. Anorder lead time profile may be customized using system 10. Pastperformance is not necessarily a good indicator of future performance.System 10 gives the user an opportunity to override or modify an orderlead time profile using client system 10. An order lead time profile maybe customized to account for maximum and minimum offered lead times. Auser may want to impose a minimum offered lead time on an order leadtime profile. An order lead time profile may be modified to reflect aminimum offered lead time by shifting the demand that is less than theminimum offered lead time to the minimum offered lead time. Moreover, auser may want to impose a maximum offered lead time on an order leadtime profile. An order lead time profile may be modified to reflect amaximum offered lead time by shifting the demand that is greater thanthe maximum offered lead time to the maximum offered lead time.

In the illustrated example, curve 160 has been modified to take intoaccount a minimum offered lead time and a maximum offered lead time toyield curves 162 and 164, respectively. Curve 162 takes into account aminimum offered lead time of 10 days, and curve 164 takes into account amaximum offered lead time of 40 days. A curve 160 of an order lead timeprofile may be modified in any other suitable manner to take intoaccount any other suitable feature. For example, order lead timeprofiles over time may be examined using a waterfall analysis todetermine trends. An order lead time profile may be adjusted to fit thetrends. As another example, an order lead time profile may be adjustedto provide a more conservative estimate or a less conservative estimate.

FIG. 7 is a bar graph 200 illustrating example cycle times for nodes 76of supply chain 70. Bar graph 200 has a y axis that represents thecumulative cycle time of a node 76, and an x axis that represents thenode 76. The cumulative cycle time represents the difference between thetime when an item reaches node 76 and the time when the end product isdelivered to customer 84. According to bar graph 200, node 76 a has acumulative cycle time of 60 days, node 76 b has a cumulative cycle timeof 30 days, node 76 c has a cumulative time of 3 days, and nodes 76 dand 76 e each have a cumulative cycle time of 0 days.

The cumulative cycle times may be used to define order lead timesegments representing a difference between cumulative cycle times.According to one embodiment, an order lead time segment may representthe difference between cumulative cycle times for successive nodes 76.According to the illustrated embodiment, order lead time segment 1represents less than or equal to 3 days, order lead time segment 2represents greater than 3 and less than or equal to 30 days, order leadtime segment 3 represents greater than 30 and less than or equal to 60days, and order lead time segment 4 represents greater than 60 days.Order lead time segments may, however, be defined in any suitablemanner.

FIG. 8 is a table 220 with example demand percentages. A demandpercentage represents the percentage of the demand that needs to besatisfied during an order lead time segment in order to satisfy an orderlead time profile.

According to the illustrated example, table 220 illustrates how tocalculate demand percentages for order lead time segments 1 through 4 ofFIG. 7 using order lead time profile curve 160 of FIG. 6. Table 220shows the range of each segment determined as described previously withreference to FIG. 7. The endpoints of each segment correspond to pointsof curve 160 of FIG. 6. For example, the three day endpoint correspondsto point P, the 30 day endpoint corresponds to point Q, and the 60 dayendpoint corresponds to point R.

Each point of curve 160 indicates a cumulative percentage of the demandthat corresponds to the number of days. For example, point P indicatesthat 33% corresponds to 3 days, point Q indicates that 90% correspondsto 30 days, and point R indicates that 100% corresponds to 60 days. Thedifference in the demand corresponding to the endpoints of the orderlead time segment yields the demand percentage. Accordingly, order leadtime segment 1 has a demand percentage of 33%−0%=33%, order lead timesegment 2 has a demand percentage of 90%−33%=57%, order lead timesegment 3 has a demand percentage of 100%−90%=10%, and order lead timesegment 4 has a demand difference of 100%−100%=0%.

FIG. 9 is a diagram illustrating an example redistributed demand for anexample supply chain 70. According to the illustrated example, thedemand may be redistributed according to table 220 of FIG. 8. The demandpercentage for OLTS1 is 33%, for OLTS2 is 57%, for OLTS3 is 10%, and forOLTS4 is 0%.

FIGS. 10 through 13 illustrate example procedures of calculatinginventory for the nodes 76 of a supply chain 70, given the demand,supply lead times, and customer service level for the nodes 76. If thedemand for a supply chain 70 is redistributed to upstream nodes 76, theinventory for the nodes 76 may be calculated for the distributed demand,which may be calculated using the demand percentages of the nodes 76.The inventory for the distributed demand may then be combined with theinventory for customer demand to obtain the total inventory for nodes76.

FIG. 10 illustrates an example supply chain portion 240 with a node 76(node 1) for which an inventory may be calculated. According to oneembodiment, the customer service level CSL for node 1 may be expressedaccording to Equation (1):

CSL=1−EBO/μ_(d)   (1)

where EBO represents the expected back order of node 1 and μ_(d)represents the mean lead time demand. Expected back order representsinsufficient inventory of node 76 to meet demand at node 76. The leadtime demand describes the demand for a lead time segment. Expected backorder EBO may be calculated according to Equation (2):

$\begin{matrix}{{EBO} = {\int_{s}^{\infty}{\left( {x - {fs}} \right){p(x)}{x}}}} & (2)\end{matrix}$

where p(x) represents the probability density function around the meanlead time demand, s represents a reorder point, and f represents apartial fulfillment factor. If partial fills are not allowed, then f=0and the term drops out. According to one embodiment, the demanddistribution may be considered a Normal distribution for relatively fastmoving items in terms of demand over lead time, a Gamma distribution foritems moving at a relatively intermediate speed in terms of demand overlead time, or a Poisson distribution for relatively slow moving items interms of demand over lead time. The distribution may be selected by auser or may be a default selection. The mean lead time demand may becalculated according to Equation (3):

$\begin{matrix}{\mu_{d} = {\int_{- \infty}^{\infty}{{{xp}(x)}{x}}}} & (3)\end{matrix}$

According to one example, for a fixed supply lead time (SLT), theinventory of node 1 may be calculated to propagate demand given the meanlead time demand μ_(d) of demand d, the standard deviation of lead timedemand s_(d) of demand d (where standard deviation is used as oneexample measure of variability), and the customer service level CSL.According to the illustrated example, mean lead time demand μ_(d) is1000 units with a variability s_(d) of 10 units, and node 1 has acustomer service level CSL of 96%. The inventory needed to cover meanlead time demand μ_(d) with x customer service level may be calculatedas μ_(d)+xs_(d), where x corresponds to y according to standardconfidence levels. For example, node 1 needs μ_(d)+2s_(d) to cover thedemand 96% of the time. In the illustrated example, the inventory neededat node 1 is μ_(d)+2s_(d)=1020 units. To satisfy the remaining demand,there is an expected back order EBO=μ_(d)×(1−CSL). In the illustratedexample, the expected back order EBO=μ_(d)×(1−CSL)=40 units. Inventorymay be calculated for a number m of time periods by multiplying theinventory units by m.

According to one embodiment, demand may be propagated to determine themean lead time demand and variability at each node 76. Then, inventorymay be calculated at individual nodes 76 using known techniques, whichmay simplify inventory optimization. In other words, a complicatedmulti-echelon supply chain problem may be reduced to a series of simplersingle echelon supply chain problems.

FIG. 11 illustrates an example supply chain portion 250 that includesone node 76 (node 1) supplying another node 76 (node 2). According tothe illustrated embodiment, node 1 has a demand d over the lead timewith a demand variability of s_(d). Node 1 has a customer service levelCSLI and a supply lead time SLT1 with a supply lead time variability ofs_(SLT1), and node 2 has a customer service level CSL2 and a supply leadtime SLT2 with a supply lead time variability of s_(SLT2).

According to one embodiment, the supply lead time for node 1 may becalculated according to Equation (4):

CSL2*SLT1+(1−CSL2)*(SLT1+SLT2)   (4)

and the supply lead time variability may be calculated according toEquation (5):

CSL2*s _(SLT1)+(1−CSL2)*(s _(SLT1) +s _(SLT2))   (5)

FIG. 12 illustrates an example supply chain portion 270 that includesone node 76 (node 3) supplying two nodes 76 (nodes 1 and 2). Node 1 hasa demand d1 with a demand variability of s_(d1) and a customer servicelevel CSLI. Node 2 has a demand d2 with a demand variability of s_(d2)and a customer service level CSL2. Node 1 has a supply lead time SLTIwith a supply lead time variability s_(SLT1), and node 2 has a supplylead time SLT2 with a supply lead time variability s_(SLT2). Node 3 hasa supply lead time SLT3 with a supply lead time variability of s_(SLT3).

According to one embodiment, supply chain portion 270 represents asingle distribution center that supports multiple distribution centersor a single intermediate item that makes multiple end-products. Thedemand at node 3 may be given by d1+d2 with a demand variability givenby Equation (6):

√{square root over (s _(d1) ² +s _(d2) ² +cov(s _(d1) ,s _(d2)))}  (6)

In a simple case, the covariance may be assumed to equal zero. Thesupply lead time and supply lead time variability of node 1 may becalculated according to Equations (4) and (5), respectively. Accordingto another embodiment, supply chain portion 270 may represent a node 76with multiple demand streams. According to this embodiment, supply chainportion 270 may represent multiple demand streams if supply lead timeSLT1=0, supply lead time variability s_(SLT1)=0, supply lead timeSLT2=0, and supply lead time variable s_(SLT2)=0. According to oneembodiment, demand of nodes 1 and 2 may be aggregated at node 3. Thedemand of nodes 1 and 2 may be pooled in order to calculate the demandof node 3.

FIG. 13 illustrates an example supply chain portion 280 that includestwo nodes 76 (nodes 2 and 3) supplying one node 76 (node 1). Node 1 hasa customer service level CSL1 and a demand d1 with a demand variabilityS_(d1). Node 2 has a customer service level CSL2 and node 3 has acustomer service level CSL3. Node 1 has a supply lead time SLT2 with asupply lead time variability s_(SLT2) from node 2, and a supply leadtime SLT3 with a supply lead time variability s_(SLT3) from node 3.

According to one embodiment, supply chain portion 280 may representproduct substitutions, alternative components, or alternate distributionroutes. According to the embodiment, supply chain portion 280 representsnode 1 receiving supplies from alternate sources nodes 2 and 3. Node 1receives a portion?, where 0=?=1, from node 2 and a portion 1-? fromnode 3. According to this embodiment, the lead time for node 1 may begiven by Equation (7):

?*SLTI+(1-?)*SLT3   (7)

with a lead time variability given by Equation (8):

?*s_(SLT1)+(1-?)*s_(SLT2)   (8)

According to another embodiment, supply chain portion 280 may representnode 1 requiring supplies from both nodes 2 and 3 to create or assemblea product. According to this embodiment, this representation of portion? is not used since node 1 requires items from both nodes 2 and 3.According to the embodiment, the lead time at node 1 may be given byEquation (9):

Max(SLT2,SLT3)   (9)

with a lead time variability given by Equation (10):

⅓[Max(SLT2+xs_(SLT2),SLT3+xs_(SLT3))−Max(SLT2,SLT3)]

where x may be determined according to standard confidence levels. Forexample, x=3 for a 99% confidence level.

To summarize, FIGS. 10 through 13 illustrate example procedures forcalculating inventory for the nodes 76 of a supply chain 70. Theinventory may be calculated given the demand, supply lead times, andcustomer service level for the node 76. If the demand for a supply chain70 is redistributed to upstream node 76, the inventory for the nodes 76may be calculated for the redistributed demand, which may be calculatedusing the demand percentages of the nodes 76. Inventory needed tosatisfy the redistributed demand may be combined with inventory neededwithout regard to the redistributed demand in order to determine thetotal demand needed at a node 76.

Certain embodiments of the invention may provide one or more technicaladvantages. For example, demand may be redistributed from an ending nodeto upstream nodes of a supply chain according to a probabilitydistribution of order lead time. Redistributing the demand to upstreamnodes may allow for optimizing inventory at individual nodes, which maysimplify the optimization. Inventory for the supply chain may beoptimized for the redistributed demand. Optimizing inventory forredistributed demand may decrease the need to stock inventory atdownstream nodes, which may minimize cost. Inventory may be optimizedwith respect to a probability distribution of order lead time for acustomer. Taking into account the order lead time may improve continuedperformance, which may lead to increased market share.

Although an embodiment of the invention and its advantages are describedin detail, a person skilled in the art could make various alterations,additions, and omissions without departing from the spirit and scope ofthe present invention as defined by the appended claims.

1. A computer-implemented method of determining a probabilitydistribution to represent order lead time, comprising: generating, usinga computer, a plurality of probability distributions of order lead timeoptions, each probability distribution of order lead time optionassociated with one of a plurality of categories; identifying, using thecomputer, a category that corresponds to a supply chain comprising aplurality of nodes, the plurality of nodes comprising a starting nodeand an ending node that supplies a customer, the supply chaindesignating a path from the starting node to the ending node; dividing,using the computer, the path into a plurality of order lead timesegments; selecting, using the computer, a probability distribution oforder lead time option associated with the identified category as aprobability distribution of order lead time of the supply chain, theprobability distribution of order lead time describing order lead timeat an ending node demand of the ending node; and determining a demandpercentage of each order lead time segment in accordance with theprobability distribution of order lead time, each demand percentagedescribing a percentage of ending node demand associated with an orderlead time segment.
 2. The method of claim 1, further comprising:associating the plurality of order lead time segments with theprobability distribution of order lead time, each order lead timesegment being associated with a corresponding order lead time range ofthe probability distribution of order lead time and wherein each demandpercentage further describing a percentage of a total ending node demandassociated with the corresponding order lead time segment.
 3. The methodof claim 1, further comprising: determining a demand percentage thatcorresponds with each order lead time segment in accordance with theprobability distribution of order lead time, each demand percentagedescribing a percentage of a total ending node demand associated withthe corresponding order lead time segment; and calculating an inventoryat each node of the plurality of nodes according to the demandpercentages of the plurality of nodes.
 4. The method of claim 1, furthercomprising: establishing a minimum offered lead time; and modifying theprobability distribution of order lead time to reflect the minimumoffered lead time.
 5. The method of claim 1, further comprising:establishing a minimum offered lead time; identifying a most upstreamstocking location in the supply chain such that the cumulative lead timefrom the stocking location to the ending node is less than the minimumoffered lead time; computing the expected percentage of demand at theending node, using the order lead time distribution for which order leadtime will be greater than the minimum offered lead time; decrementingthe demand at the ending node by this computed percentage; andcalculating a safety stock at the ending node using the decrementeddemand.
 6. The method of claim 1, further comprising: establishing amaximum offered lead time; and modifying the probability distribution oforder lead time to reflect the maximum offered lead time.
 7. The methodof claim 1, further comprising: establishing a maximum offered leadtime; identifying a portion of ending node demand corresponding to anorder lead time range greater than the maximum offered lead time; andshifting the portion of ending node demand to the maximum offered leadtime in order to modify the probability distribution of order lead timeto reflect the maximum offered lead time.
 8. A system of determining aprobability distribution to represent order lead time, comprising: adatabase configured to store a plurality of probability distributions oforder lead time options, each probability distribution of order leadtime option associated with one of a plurality of categories; and acomputer system coupled with the database and configured to: identify acategory that corresponds to a supply chain comprising a plurality ofnodes, the plurality of nodes comprising a starting node and an endingnode that supplies a customer, the supply chain designating a path fromthe starting node to the ending node; divide the path into a pluralityof order lead time segments; select a probability distribution of orderlead time option associated with the identified category as aprobability distribution of order lead time of the supply chain, theprobability distribution of order lead time describing ending nodedemand of the ending node versus order lead time; and determine a demandpercentage of each order lead time segment in accordance with theprobability distribution of order lead time, each demand percentagedescribing a percentage of ending node demand associated with an orderlead time segment.
 9. The system of claim 8, the computer system furtherconfigured to: associate the plurality of order lead time segments withthe probability of order lead time, each order lead time segment beingassociated with a corresponding order lead time range of the probabilitydistribution of order lead time and wherein each demand percentagefurther describing a percentage of a total ending node demand associatedwith the corresponding order lead time segment.
 10. The system of claim8, the computer system further configured to: determine a demandpercentage of each order lead time segment in accordance with theprobability distribution of order lead time, each demand percentagedescribing a percentage of a total ending node demand associated withthe corresponding order lead time segment; and calculate an inventory ateach node of the plurality of nodes according to the demand percentagesof the plurality of nodes.
 11. The system of claim 8, the computersystem further configured to: establish a minimum offered lead time; andmodify the probability distribution of order lead time to reflect theminimum offered lead time.
 12. The system of claim 8, the computersystem further configured to: establish a minimum offered lead time;identify a portion of ending node demand corresponding to an order leadtime range less than the minimum offered lead time; and shift theportion of ending node demand to the minimum offered lead time in orderto modify the probability distribution of order lead time to reflect theminimum offered lead time.
 13. The system of claim 8, the computersystem further configured to: establish a maximum offered lead time; andmodify the probability distribution of order lead time to reflect themaximum offered lead time.
 14. The system of claim 8, the computersystem further configured to: establish a maximum offered lead time;identify a portion of ending node demand corresponding to an order leadtime range greater than the maximum offered lead time; and shift theportion of ending node demand to the maximum offered lead time in orderto modify the probability distribution of order lead time to reflect themaximum offered lead time.
 15. A non-transitory computer-readable mediumembodied with software for determining a probability distribution torepresent order lead time, the software when executed using a computeris configured to: generate a plurality of probability distributions oforder lead time options, each probability distribution of order leadtime option associated with one of a plurality of categories; identify acategory that corresponds to a supply chain comprising a plurality ofnodes, the plurality of nodes comprising a starting node and an endingnode that supplies a customer, the supply chain designating a path fromthe starting node to the ending node; divide the path into a pluralityof order lead time segments; select a probability distribution of orderlead time option associated with the identified category as aprobability distribution of order lead time of the supply chain, theprobability distribution of order lead time describing ending nodedemand of the ending node versus order lead time; and determine a demandpercentage of each order lead time segment in accordance with theprobability distribution of order lead time, each demand percentagedescribing a percentage of ending node demand associated with an orderlead time segment.
 16. The computer-readable medium of claim 15, furtherconfigured to: associate the plurality of order lead time segments withthe probability distribution of order lead time, each order lead timesegment being associated with a corresponding order lead time range ofthe probability distribution of order lead time and wherein each demandpercentage further describing a percentage of a total ending node demandassociated with the corresponding order lead time segment.
 17. Thecomputer-readable medium of claim 15, further configured to: determine ademand percentage of each order lead time segment in accordance with theprobability distribution of order lead time, each demand percentagedescribing a percentage of a total ending node demand associated withthe corresponding order lead time segment; and calculate an inventory ateach node of the plurality of nodes according to the demand percentagesof the plurality of nodes.
 18. The computer-readable medium of claim 15,further configured to: establish a minimum offered lead time; and modifythe probability distribution of order lead time to reflect the minimumoffered lead time.
 19. The computer-readable medium of claim 15, furtherconfigured to: establish a minimum offered lead time; identify a portionof ending node demand corresponding to an order lead time range lessthan the minimum offered lead time; and shift the portion of ending nodedemand to the minimum offered lead time in order to modify theprobability distribution of order lead time to reflect the minimumoffered lead time.
 20. The computer-readable medium of claim 15, furtherconfigured to: establish a maximum offered lead time; and modify theprobability distribution of order lead time to reflect the maximumoffered lead time.